Predistortion control apparatus

ABSTRACT

A digital predistorter comprises a module J for producing a counteracting signal V m1  for combination with the input signal of a power amplifier to correct the output of the amplifier for distorting memory effects within the amplifier. The module J produces the contracting signal V m1  by convolving (see FIG.  6 ) functions of the input signal with impulse response characteristics related to the memory effects being corrected. The counteracting signal V m1  is produced by a function f m  and parameters in that function are adjusted to minimise any residual distortion in the amplifier output.

The present invention relates to apparatus for, and methods of,controlling a predistorter that operates on an input signal to an itemof signal handling equipment, such as a power amplifier in a mobileradio telephone, in order to reduce the amount of distortion that theequipment causes in an output signal produced in response to the inputsignal.

It is known to perform predistortion of power amplifier input signals inthe digital domain. The digital predistorter is finding increased usagein linearising RF power amplifiers and this is partly due to the recentavailability of high sampling rate Analogue to Digital converters (ADCs)and Digital to Analogue converters (DACs) and corresponding improvementsin the speed of Digital Signal Processing (DSP) hardware which make thisform of linearisation possible. It is also due to the increasing use ofnon-constant envelope modulation schemes and the ever important need toincrease amplifier efficiency which makes this form of linearisationdesirable.

However, most conventional predistorters only correct for amplifierdistortion that is a function of the instantaneous signal amplitude.This is commonly referred to as AM (Amplitude Modulation) to AM and AMto PM (Phase Modulation) distortion. This form of predistorter, whenimplemented digitally, often operates with two look-up tables (foradjusting, for example, the gain and phase of the amplifier inputsignal) which are indexed by the signal amplitude (or some function ofthe input amplitude) and which then act to modify the amplitude andphase of the signal applied to the amplifier input so as to counter itsdistortion.

Unfortunately many real amplifiers exhibit distortion that is a functionof the signal in the past as well as the present. These amplifiers aresaid to possess memory. The AM-AM and AM-PM type predistorter describedabove will have limited performance when linearising an amplifier thatexhibits memory since it can only correct for that component of thedistortion which can be expressed as a function of the instantaneoussignal amplitude.

In general, the amplifier memory effect will become more significant asthe signal bandwidth increases and the conventional AM-AM and AM-PMpredistorter performance will therefore get correspondingly worse. Sincethere is often a tendency for signal bandwidth to increase (particularlyin the area of mobile telecommunications) the problem of memory effectdistortion, and its correction, is now becoming a major problem for RFpower amplifier design.

A predistorter capable of counteracting memory effect distortion can bedevised and one aim of the invention is to provide a scheme forcontrolling such a predistortion technique.

According to one aspect, the invention provides apparatus forcontrolling a predistorter, said predistorter being arranged to apply apredistortion to an input signal to signal handling equipment to countermemory-effect distortion in an output signal of said equipment, whereinsaid predistortion is at least partially defined by a set of one or moreparameters and the apparatus comprises adjusting means for adjustingsaid set to determine how adjustments to said set change said distortionand control means for deploying an adjusted version of said set in saidpredistorter that reduces said distortion.

The invention also consists in a method of controlling a predistorter,said predistorter being arranged to apply a predistortion to an inputsignal to signal handling equipment to counter memory-effect distortionin an output signal of said equipment, wherein said predistortion is atleast partially defined by a set of one or more parameters and themethod comprises adjusting said set to determine how adjustments to saidset change said distortion and deploying an adjusted version of said setin said predistorter that reduces said distortion.

In a preferred embodiment, the process of adjusting the set involvespredicting how adjustments to said set would change said distortion andthe version of the set that is then deployed in the predistorter is aversion of said set that is predicted to reduce said distortion. Thus,the predistortion control technique can allow one or more parametersspecifying the predistortion to be updated without perturbing theoperation of the predistorter during the period when updated parametervalues are being calculated.

In another embodiment, the adjustment of the set is done in thepredistorter itself, so the process of adjusting the set may perturb theoperation of the predistorter.

In a preferred embodiment, the prediction process is used to identify achange to the set that minimises the distortion. The minimisingadjustment can then be applied to the parameter set being used in thepredistorter. It will be appreciated that the accuracy of themninimisation of the distortion is limited by the capabilities of theparticular method used to find the minimum distortion point.

In one embodiment, the effect of an adjustment to the set is predictedby calculating how an adjustment to said set will change a time domainquantity indicative of said distortion in order to predict how saiddistortion will change. Preferably, said quantity is a normalisedaverage of the magnitude of an error in said output signal.

In one embodiment, the effect of an adjustment to the set is predictedby calculating how an adjustment to said set will change a frequencydomain quantity indicative of said distortion in order to predict howsaid distortion will change. Preferably, said quantity is a measure ofthe average of the power in said output signal that lies outside a rangeof desired frequencies. The desired range of frequencies may be therange occupied by the input signal before it gets distorted by thesignal handling equipment.

In one embodiment, the predistortion is partly defined by a function ofsaid input signal in which said set appears and the effect of anadjustment to the set is predicted by calculating how an adjustment tosaid set will change said function and using the change in the functionto predict how said distortion will change.

In one embodiment, the predistortion is partly defined by a function ofsaid input signal in which said set appears and said function shapessaid predistortion by way of convolving an impulse responsecharacteristic with another function of the input signal to produce acorrection signal and subtracting from the correction signal theexpectation value of said correction signal at the current state of saidinput signal in order to produce a difference signal that is used toproduce the predistortion.

In preferred embodiments of the invention, the signal handling equipmentupon which the linearising technique of the invention operates is apower amplifier or an arrangement of several of such.

By way of example only, certain embodiments of the invention will now bedescribed with reference to the accompanying figures, in which:

FIG. 1 is a block diagram showing the basic structure of a prior artpredistorter;

FIG. 2 is a block diagram showing the basic structure of a predistortercapable of performing memory-effect correction;

FIG. 3 is a vector diagram showing signals in an amplifier to belinearised;

FIG. 4 is a block diagram showing the structure of a Cartesian versionof the predistorter of FIG. 2 in more detail;

FIG. 5 is a block diagram showing the structure of a polar version ofthe predistorter of FIG. 2 in more detail;

FIG. 6 is a block diagram showing the generic form of the functions f₁and f₂ used in FIGS. 4 and 5;

FIG. 7 shows a variant of the structure of the functions f₁ and f₂ givenin FIG. 6;

FIG. 8 shows another variant of the structure of the functions f₁ and f₂given in FIG. 7;

FIG. 9 shows an overview of a system for addressing both memory effectand instantaneous distortion and in particular shows elements forcontrolling memory effect predistortion;

FIG. 10 is a flow diagram of a control algorithm for the memory effectpredistorter of FIG. 2 based on the minimisation of a quantity in thetime domain; and

FIG. 11 is a flow diagram of a control algorithm for the memory effectpredistorter of FIG. 2 based on the minimisation of a quantity in thefrequency domain.

The basic building blocks of a prior art digital predistorted amplifierare shown in FIG. 1. This form of predistorter often operates with twolook-up tables (for adjusting, for example, the gain and phase of theamplifier input signal) which are indexed by the signal amplitude, orsome function of the input amplitude, and which then act to modify theamplitude and phase of the signal applied to the amplifier input so asto counter its distortion. However, this form of predistorter will onlycorrect for amplifier distortion which is a function of theinstantaneous amplitude of the input signal. Such distortion is commonlyreferred to as AM (Amplitude Modulation) to AM and AM to PM (PhaseModulation) distortion and is referred to herein as instantaneousdistortion.

Unfortunately, many real amplifiers exhibit distortion which is afunction of the signal in the past as well as the present and theseamplifiers are said to possess “memory”. The “instantaneous distortion”type predistorter known from the prior art described above will havelimited performance when linearising an amplifier which exhibits thismemory effect.

In FIG. 1, the RF input signal RF₁ to the amplifier A is, if necessary,down-converted in frequency and then converted into a digital signal S₁at the A/D block. S₁ is supplied to a predistorter function B and alsoto control block C. The predistorter B alters S₁ into S₃ whichsubsequently undergoes conversion back to the analogue domain at the D/Ablock and, if necessary, frequency up-conversion before being suppliedto the amplifier A. The linearised output RF₂ of amplifier A is thensampled by control block C as signal S₂ using appropriate A/D conversionand, if necessary, frequency down-conversion. Block C compares thesignals S₁ and S₂ and uses the result to adapt the operation ofpredistorter B to optimise linearisation of RF₂.

FIG. 2 illustrates the basic architecture of the modified digitalpredistorter (B) which incorporates correction for both theinstantaneous distortion signal and the memory distortion signal.

It can be seen that the modification to the predistorter which performsmemory distortion correction involves a functional block J placed justprior to the AM-AM and AM-PM predistorter. In other words, there are nochanges required to the AM-AM and AM-PM predistorter block. Thisprovides the advantage that an existing predistorter product can beretrofitted in a relatively simple matter with a memory effectpredistorter according to an embodiment of the present invention.

In block J, delay 1 compensates for delays in blocks D and E and T isthe sample period and MT is the maximum time interval over whichcontribution to V_(m) (the output signal error component attributable tothe memory effect) is non negligible.

If the predistorter is turned off (such that it acts as a linear gainstage), then the signal appearing at the output of the amplifier at anyinstant in time can be represented in phase and amplitude on a vectordiagram as illustrated in FIG. 3.

The following vectors are shown in FIG. 3:

V_(w) is the linearly amplified output vector as would be output by anideal, non distorting amplifier.

V_(ins) is the distortion vector which is simply a function of theinstantaneous input signal amplitude (this represents AM to AM and AM toPM distortion). This will be called the instantaneous distortion vector.

V_(m) is the distortion vector which is a function of the input signalat times in the past as well as the present. This will be called thememory distortion vector.

V_(n) is an error vector due to system noise figure, digitisingquantisation noise, gain and phase ripple, unwanted spurious signalsetc. This error vector cannot be removed by predistortion and representsthe residual distortion remaining after conventional predistortion andmemory compensation have been applied.

V_(error) is the total error vector taking into account all contributingerror vectors.

|V₁| is the input signal amplitude, so we can write:

-   -   V_(ins)=f_(ins)(|V₁|).

Also, V_(m) can be more precisely expressed as:V _(m) =f _(m)(V ₁(t), V ₁(t−δt), V ₁(t−2δt) . . . V₁(t−M.δt))_(lim δt→0)  (1)where M.δt is the memory duration, i.e. the longest interval over whichthe contribution to V_(m) is non-negligible.

V_(m) has the property that its expectation value when evaluated at anyinput amplitude is zero. This can be expressed asE{V _(m) } _(|V) ₁ ₅₁ =0  (2)

The function E{V}_(|V) ₁ _(|) is the expectation value or mean value ofV when evaluated at some amplitude |V₁|.

The purpose of the predistorter is to distort the signal (or vector) atthe amplifier input such that the signal at the amplifier output has anadditional vector present which is equal and opposite to the totaldistortion vector produced by the amplifier. In this way the netdistortion vector present at the amplifier output is zero (ideally).

Since the instantaneous distortion vector V_(ins) can be defined as afunction of only the instantaneous input amplitude |V₁| i.e.V_(ins)=f(|V₁|) it follows that in order to predistort and remove thisvector at the amplifier output we need a predistorter which is also afunction of the instantaneous input amplitude. If V₁ at any instant oftime is expressed as a complex quantity:

-   -   V₁=A₁exp(jθ₁) where A₁=|V₁|        then the predistorter output V₃ can be written        V ₃ =G _(p)(A ₁).A ₁exp(jθ₁ +jP _(p)(A ₁))  (3)        where G_(p)(A₁) and P_(p)(A₁) represent the amplitude dependent        gain and phase shift of the predistorter.

If we also represent the amplifier amplitude dependent gain and phaseshift as G_(A)(A₁) and P_(A)(A₁) then the predistortion is optimum forthe instantaneous distortion vector (V_(ins)=0) when the amplifieroutput can be written asV ₂ =G _(A)(G _(p)(A ₁).A ₁).G _(p)(A ₁).A ₁.exp(jθ ₁ +jP _(p)(A ₁)+jP_(A)(G _(p)(A ₁).A ₁))  (4)where:G _(A)(G_(p)(A ₁).A ₁).G _(p)(A ₁)=G ₀=constant   (5)and:P _(p)(A ₁)+P _(A)(G _(p)(A ₁).A ₁)=Θ₀=constant (=0 for simplicity)  (6)

A common way of implementing the predistorter correction for V_(ins) isthrough the use of look-up tables for G_(p)(A₁) and P_(p)(A₁) and whichsatisfy equations 5 and 6. Alternatively, if the predistorter isimplemented using Cartesian -signals we use look-up tables LI(A₁) andLQ(A₁) such thatV ₃ ={LI(A ₁)+j. LQ(A₁)}.A ₁.exp(j θ ₁)  (7)and whereG _(p)(A ₁l)={LI(A ₁)² +LQ(A)²}^(1/2)  (8)P _(p)(A ₁)=tan⁻¹(LQ(A ₁)/LI(A ₁))  (9)

Removing the memory distortion vector V_(m) from the amplifier outputcan be achieved by adding a signal vector V_(m1)/G₀ to the predistorterinput signal V₁. In this way the output of the amplifier when thepredistorter look-up tables G_(p) and P_(p) (or LI and LQ) satisfyequations 5 and 6 is:V ₂ =G ₀ .V ₁ +V _(m1) +V′ _(m) +V _(n)  (10)where V′_(m) is the memory distortion vector which is now slightlydifferent from V_(m) owing to the predistortion of V₁. However, V′_(m)will still have the same form as equation 1 and will satisfy equation 2.

If V_(m1) is chosen such that V_(m1)=V′_(m) then we are left withV ₂ =G ₀ .V ₁ +V _(n)   (11)

In other words the amplifier non-linearity signals have been removed andwe have at the amplifier output a linearly amplified input signal andnoise.

The function to be evaluated in block D of FIG. 2 is therefore of theform:

-   -   f_(m)(V₁(t), V₁(t−δt), V₁(t−2δt) . . . V₁(t−Mδt))_(lim δt→0).        and must satisfy the condition E{ƒ_(m)( )}_(|v) ₁ _(|)=0.

The function f_(m)( ) will, in general, be a mixture of linear andnon-linear processes and some specific embodiments for this function aresummarised below.

In general, the function f_(m)( ), the function implemented by block Dof FIG. 2, will be a mixture of linear and non-linear processes and itsdetailed implementation will vary according to the characteristics ofthe specific amplification device being used. In FIGS. 4 and 5, f_(m)( )is shown in a form that will facilitate implementation in an FPGA (FieldProgrammable Gate Array) or ASIC (Application Specific IntegratedCircuit).

A generic Cartesian implementation of f_(m)( ) is presented in FIG. 4which is sufficiently general to cover the majority of amplificationdevices. The function E{V}_(|v) ₁ _(|) is the expectation value or meanvalue of V when evaluated at the input amplitude |V₁|. Depending on theform of f_(m)( ) it may be possible to express E{V_(14I)}_(|v) ₁ _(|)and E{V_(14Q)}_(|v) ₁ _(|) as relatively simple functions of V₁ for easeof calculation. E{V_(14I)}_(|v) ₁ _(|) is subtracted from f₁ to producea first difference signal and E{V_(14Q)}_(|v) ₁ _(|) is subtracted fromf₂ to produce a second difference signal. The subtraction of thequantities E{V_(14I)}_(|v) ₁ _(|) and E{V_(14Q)}_(|v) ₁ _(|) ensuresthat E{V_(m)}_(|v) ₁ _(|)=0 or E{ƒ_(m)( )}_(|v) ₁ _(|)=0 as required.The difference signal produced in the f₁ path is multiplied with theversion of V₁ passing through block D. The difference signal produced inthe f₂ path is multiplied with a version of V₁ that has been offset by90 degrees. The outputs of the two multiplication processes are thensummed to produce V_(m1).

A generic polar implementation of f_(m)( ) is presented in FIG. 5 whichis sufficiently general to cover the majority of amplification devices.The subtraction of E{V_(14A)}_(|v) ₁ _(|) and E{V_(14P)}_(|v) ₁ _(|)ensures that E{V_(m)}_(|v) ₁ _(|)=0 or E{ƒ_(m)( )}_(|v) ₁ _(|)=0 asrequired. The difference signal produced in the f₂ path is used tomodulate the phase of the version of V₁ passing through block D. Thedifference signal produced in the f₁ path is offset by +1 and then usedto modulate the amplitude of the version of V₁ passing through block D.

Clearly, if functional block J (FIG. 2) is modified by removing thedirect path for V₁ then in this embodiment of f_(m)( ) the subtractionof V₁ just prior to output of V_(m1) is unnecessary.

The nature of the functions f₁ and f₂ employed in FIGS. 4 and 5 will nowbe discussed in more detail with reference to FIGS. 6, 7 and 8.

FIG. 6 shows the general form used for both of the functions f₁ and f₂.V₁ is supplied to each of a number of paths where signal processing isperformed. The outputs of the paths are then summed to produce signalV₁₄. There can be as many paths as required. Each path operates on V₁ toproduce initially a signal, e.g. V₁₂₁, which is a function of V₁, whichis then convolved with a filter impulse response, e.g. H₁(t), to producea further signal, e.g. V₁₃₁, which is in turn processed such that afunction, e.g. f_(n21), of that signal issues from the path to thesummation point. It will be apparent that f₁ need not be the same as f₂,for example f_(n11) for f₁ and f₂ need not be the same.

The preferred generic embodiment of functions f₁ and f₂ can besignificantly simplified if we make a number of assumptions relating tothe physical cause of the amplifier memory effect. If we assume that thememory effect is due to modulation of the amplitude or phase of thesignal and the modulation is linearly proportional to the value of asingle physical variable (such as device temperature or bias voltage)and if we assume the physical variable is a function of the mean current(I_(m)) through the amplifying device and the function has an impulseresponse of the form e^(−t/τ), then the form of f₁ and f₂ can besimplified to that shown in FIG. 7.

In many cases it is a good approximation to make I_(m)(t)≈|V₁(t)|² andit should be noted that in general the time constant τ and coefficientb₁ will be different for functions f₁ and f₂.

If we assume that the amplifier memory effect is due to modulation ofthe amplitude or phase of the signal and the modulation is linearlyproportional to the value of several physical variables (such as devicetemperature, bias voltage etc.) and if we assume the physical variablesare separate functions of the mean current (I_(m)) through theamplifying device and the functions have an impulse response of the forme^(−t/τ) then the form of f_(m)( ) can be simplified to that shown inFIG. 8. It is assumed that the mean current is averaged over a timeinterval significantly longer than the carrier period and significantlyshorter than the period of the maximum modulation signal frequency.Depending on the amplification device it may again be valid toapproximate I_(m)(t) as |V₁(t)|².

In particular the situation postulated in the preceding paragraph canoccur when the memory vector is made up from a number of memory effectsat differing time-constants. This is likely to be the situation for mostpower amplifiers, as memory effects will result from thermal issues inthe power device(s) and bias interaction with the range of de-couplingcapacitors typically used on the gate and drain of, for example, an FETdevice. Each of these (the thermal and multiple capacitor-basedtime-constants) will result in a memory vector which has a differenttime constant.

It is worth noting that, to the skilled person, it will be apparent thatthe predistorter functions used for instantaneous distortion vectorcorrection and memory distortion vector correction could bepre-programmed and then subsequently left unchanged. Such an ‘open loop’predistorter will work satisfactorily when the amplifier distortioncharacteristics do not change with time, temperature etc or when onlysmall linearity improvements are required. However, adaptive control ofthe predistorter for both instantaneous and memory distortion vectors isdesirable when changes to the amplifier distortion characteristics areexpected. A number of control schemes for the look up tables G_(p) andP_(p) (see equation 3 above)—or LI and LQ if control is implemented inthe Cartesian format—have been documented and will not be discussedagain here.

We will now describe some control schemes that are suitable forcontrolling the memory effect predistortion blocks in the systemsdescribed above. FIG. 9 shows an overview of the system of FIG. 2 andincludes the elements responsible for controlling the memory effectpredistorter. In FIG. 9, a control block F receives successive pairs ofsamples of the input and output signals V₁ and V₂. Block F uses seriesof pairs of these values to update a set of parameters P that controlthe memory effect predistorter J. The process of determining the updatedset of parameters P_(new) involves manipulating P and testing to see ifthe changes to P would improve the operation of the memory effectpredistorter J. Block F calculates the revised parameters P_(new) in aseparate process operating alongside the predistorter J and the revisedparameters P_(new) are then loaded into the memory effect predistorter.Thus, the process of determining the new parameters P_(new) does notrequire changing the actual parameters P that are being used within thememory effect predistorter J which would degrade the performance ofpredistorter J whilst the revised parameters P_(new) were beingcalculated.

Since, by definition E{V_(m1)}_(|V) ₁ _(|)=0, any changes to the controlparameters of the memory effect predistorter J will not affect theinstantaneous predistorter B. Thus the memory effect predistorter J canbe controlled independently of the instantaneous predistorter B, withoutcontrol adjustments to one of the predistorters degrading the signalcorrection being performed by the other one of the predistorters.

The control scheme for the memory effect predistorter J operates byusing a fixed form for f_(m)( ), the function implemented by block D inFIG. 2, but with variable function parameters. For example, a functionwith a fixed form and variable parameter is ƒ(x)=ax^(b+cx) ^(d) where band d are fixed serving to set the form of the function but a and c arevariable parameters. The optimum set of function parameters for f_(m)( )is then found by block F by minimising a quantity which relates to themagnitude of the memory vector (V_(m)) at the amplifier output.

The quantity to be minimised may be calculated in either the frequencyor the time domain and there are advantages and disadvantages with eachapproach. If the magnitude of V_(m) is significant compared to the totalerror vector (V_(error)) then the average magnitude of V_(error) can beused as the quantity to be minimised. This is readily obtained bycomparing V₁ and V₂ in the time domain. Alternatively, if the magnitudeof V_(m) is significant compared to the total error vector there will bea significant contribution to the ‘out-of-band’ signal power (i.e.outside the wanted signal bandwidth) as seen in the frequency domain. Aquantity relating to the signal power in a range of frequencies outsidethe wanted signal bandwidth can therefore also be used as the quantityto be minimised.

Preferred embodiments for the algorithms used by block F to determinethe optimum set of parameters to be used in the predistorter memoryfunction f_(m)( ) will now be discussed.

FIG. 10 shows a control algorithm for updating the parameters P of thememory effect predistorter J based on the minimisation of a quantity inthe time domain. This algorithm is performed by control block F uponreceipt from block C of a series of successive samples of the input andoutput signals V₁ and V₂ of the amplifier and results in updatedparameters P_(new) for use in the function f_(m)( ) and calculated tocause the minimisation of V_(m).

With reference to FIG. 10, the algorithm commences with a loop whichwaits for the operation of the instantaneous predistorter B to settle toa steady state. Once this has occurred, the algorithm continues bycapturing n successive pairs of samples of the input and output signals(V₁ and V₂) . Then, the time delay and the phase offset between thecaptured samples of V₁ and V₂ are removed.

Next, the algorithm enters a minimisation loop that aims to minimise${E\{ \frac{V_{error}}{V_{1}} \}},$the mean of the error vector magnitude normalised by the input signalmagnitude with averaging done over the sample pairs of V₁ and V₂. InFIG. 10, this loop is shown only figuratively. For example, the flowchart does not show the details of how one tests for a minimum in${E\{ \frac{V_{error}}{V_{1}} \}},$partly for the sake of clarity and partly because such a test can beperformed in any of a number of ways.

The first step in the minimisation loop is the selection a new set ofparameters P_(nom) for the function f_(m)( ) to replace the set ofparameters P₀ currently being used in the predistorter. The details ofhow one selects the new values of the parameters depends on the detailsof the process employed for testing for a minimum in$E{\{ \frac{V_{error}}{V_{1}} \}.}$Having nominated a new set of parameters P_(nom), the algorithm thenproceeds to evaluate the function Δf_(m) which is the change in f_(m)when the parameters of the function change from P₀ to P_(nom), i.e.Δf_(m)=f_(m)(P_(nom))−f_(m)(P₀). The next step within the minimisationloop is the evaluation of the quantity$E\{ \frac{V_{error}}{V_{1}} )$at the set of parameters P_(nom), i.e. the algorithm now calculates$E{\{ \frac{{V_{2} - {G_{0}.V_{1}} + {\Delta\quad{f_{m}{()}}}}}{V_{1}} \}.}$The next step within the minimisation loop is to check if$E\{ \frac{{V_{2} - {G_{0}.V_{1}} + {\Delta\quad{f_{m}{()}}}}}{V_{1}} )$is a minimum. If not, the algorithm returns to the step of selecting anew set of parameters P_(nom), selects a new set and proceeds withevaluating$E\{ \frac{{V_{2} - {G_{0}.V_{1}} + {\Delta\quad{f_{m}{()}}}}}{V_{1}} )$for the new set.

Thus, the minimisation loop basically checks to see if$E\{ \frac{{V_{2} - {G_{0}.V_{1}} + {\Delta\quad{f_{m}{()}}}}}{V_{1}} )$is a minimum as Δf_(m)( ) is varied by varying P_(nom). When thealgorithm exits the minimisation loop, the set of parameters P_(nom)that minimised $E\{ \frac{V_{error}}{V_{1}} )$becomes P_(new) and is loaded into block D for generating V_(m1).P_(new) then becomes P₀ in preparation for the next time that the systemcarries out the algorithm of FIG. 10.

FIG. 11 shows a control algorithm for the memory effect predistorter Jbased on the minimisation of a quantity in the frequency domain. Thiscontrol scheme operates in a similar manner to that described withreference to FIG. 10 but the quantity that is minimised is instead ameasure of the power in V₂ that lies outside the desired bandwidth ofV₂. To obtain this quantity, the digital Fourier transform (DFT) of thesignal quantity V₂+Δf_(m)( ) is calculated and the power U contained ina range of frequencies f outside the wanted signal bandwidth isdetermined:$U = {\sum\limits_{f}\quad{{{DFT}\lbrack {V_{2} + {\Delta\quad{f_{m}{()}}}} \rbrack}}^{2}}$

The algorithm operates to provide a parameter set P_(new) whichminimises U.

1-16. (canceled)
 17. Apparatus for controlling a predistorter, saidpredistorter being arranged to apply a predistortion to an input signalto signal handling equipment to counter memory-effect distortion in anoutput signal of said equipment, wherein said predistortion is at leastpartially defined by a function that includes a set of one or moreparameters and the apparatus comprises adjusting means for adjustingsaid set to determine how adjustments to said set change said distortionand control means for deploying an adjusted version of said set in saidpredistorter that reduces said distortion.